Problem: Solve for $x$ and $y$ using elimination. ${4x+3y = 10}$ ${-5x-3y = -11}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-x = -1$ $\dfrac{-x}{{-1}} = \dfrac{-1}{{-1}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {4x+3y = 10}\thinspace$ to find $y$ ${4}{(1)}{ + 3y = 10}$ $4+3y = 10$ $4{-4} + 3y = 10{-4}$ $3y = 6$ $\dfrac{3y}{{3}} = \dfrac{6}{{3}}$ ${y = 2}$ You can also plug ${x = 1}$ into $\thinspace {-5x-3y = -11}\thinspace$ and get the same answer for $y$ : ${-5}{(1)}{ - 3y = -11}$ ${y = 2}$